Tunnels and long corridors are challenging environments for mobile robots because a LiDAR point cloud should degenerate in these environments. To tackle point cloud degeneration, this study presents a tightly-coupled LiDAR-IMU-wheel odometry algorithm with an online calibration for skid-steering robots. We propose a full linear wheel odometry factor, which not only serves as a motion constraint but also performs the online calibration of kinematic models for skid-steering robots. Despite the dynamically changing kinematic model (e.g., wheel radii changes caused by tire pressures) and terrain conditions, our method can address the model error via online calibration. Moreover, our method enables an accurate localization in cases of degenerated environments, such as long and straight corridors, by calibration while the LiDAR-IMU fusion sufficiently operates. Furthermore, we estimate the uncertainty (i.e., covariance matrix) of the wheel odometry online for creating a reasonable constraint. The proposed method is validated through three experiments. The first indoor experiment shows that the proposed method is robust in severe degeneracy cases (long corridors) and changes in the wheel radii. The second outdoor experiment demonstrates that our method accurately estimates the sensor trajectory despite being in rough outdoor terrain owing to online uncertainty estimation of wheel odometry. The third experiment shows the proposed online calibration enables robust odometry estimation in changing terrains.